Origins of the Mach–Poincaré Principle

The problem with the definition of inertia was solved, in the simple case of free point particles, by Tait, who introduced the concept of inertial frame. Tait’s solution would have satisfied Leibniz’ request that inertia be determined dynamically, however it only works in the absence of interactions between the material bodies. Later Mach posed again the question of the origin of inertia, suggesting the idea that it should be dynamical, which was later dubbed ‘Mach’s principle’. Moreover Mach criticized also Newton’s absolute time, and introduced the basic idea of temporal relationalism, i.e. that time should be a concept that is abstracted from change and has no independent existence. This idea is at the basis of SD and many other relational approaches to physics. This chapter concludes with the Barbour–Bertotti formulation of Mach’s principle, which they called ‘Mach–Poincaré Principle’. This formulation removes the vagueness of Mach’s original idea, and puts the principle into a precise mathematical form, which is one of the basic axioms of SD.